Question

Represent these numbers on the number line
(i) \[\dfrac{7}{4}\]
(ii) \[ - \dfrac{5}{6}\]

Answer 1

Hint:
We will identify 2 integers between which the given fraction lies. Then if the numerator of the fraction is greater than the denominator, we will express the fraction in mixed form. Next, we will look at the denominator of the fraction. We will divide the space between the 2 integers into \[D\] equal parts where \[D\] is the denominator of the fraction. We will be able to represent the fraction on the number line easily after this step.

Complete step by step solution:
i. We know that \[\dfrac{7}{4}\] is approximately equal to \[1.7\]. The 2 integers between which \[\dfrac{7}{4}\] lies are 1 and 2.

Also \[\dfrac{7}{4}\] can be expressed as \[1\dfrac{3}{4}\].
The denominator of \[\dfrac{7}{4}\] is 4. Let’s divide the space between 1 and 2 into 4 equal parts.

We can see that \[1\dfrac{3}{4}\]is the third tick on the right of 1.

We have represented \[\dfrac{7}{4}\]in the number line with a red tick.
ii. \[ - \dfrac{5}{6}\] is approximately equal to \[ - 0.83\]. The 2 integers between which \[ - \dfrac{5}{6}\] lies are 0 and \[ - 1\].

As the numerator of the fraction is less than the denominator, we cannot express it in mixed form. The denominator of the fraction is 6. Let us divide the space between 0 and \[ - 1\] into 6 equal parts.

We can see that \[ - \dfrac{5}{6}\] is the 1st tick on the right side of \[ - 1\].

We have represented \[ - \dfrac{5}{6}\]on the number line with a red tick.

Note:
On a number line, the numbers to the right side of 0 are positive numbers and numbers to the left side of 0 are negative numbers. When we are dealing with negative numbers, we must be careful that a number with a greater magnitude is smaller than a number which has less magnitude. For example, \[ - 8\] is greater than \[ - 9\] even though 8 is smaller than 9.